Find the Exact Value cot(405)

Problem

cot(405)

Solution

1. Identify the angle as being greater than 360 and find its coterminal angle within the range [0,360)

2. Subtract 360 from the given angle to find the coterminal angle.

405−360=45

3. Recognize that the trigonometric functions of coterminal angles are equal.

cot(405)=cot(45)

4. Apply the definition of the cotangent function, which is the reciprocal of the tangent function.

cot(45)=1/tan(45)

5. Substitute the known exact value for tan(45) which is 1

cot(45)=1/1

6. Simplify the expression to find the final value.

cot(45)=1

Final Answer

cot(405)=1

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